nLab
quantum sheaf cohomology

Context

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

Quantum field theory

Contents

Idea

Gromov-Witten theory may be understood as providing a product on formal power series over certain abelian sheaf cohomology groups of Kähler manifolds XX. The quantum cohomology of XX is the resulting Frobenius algebra structure on these formal power series.

Together with Gromov-Witten theory quantum sheaf cohomlogy was discovered in and has its geometric roots as part of the data that describes certain 2-dimensional sigma-model quantum field theories with target space XX.

References

An introduction for readers familiar with basic concepts of Gromov-Witten theory is in

  • Josh Guffin, Quantum sheaf cohomology, a précis (pdf)

Slides of a talk for an audience of mathematical string theorists are

  • Eric Sharpe,

    Quantum sheaf cohomology (pdf) Brandeis university (2010)

    Quantum sheaf cohomology I (pdf)

Revised on January 5, 2014 15:14:42 by Urs Schreiber (82.113.121.83)